SOLUTION: Can someone please show me how to do this problem? -4<6-2x<4

Question 261547: Can someone please show me how to do this problem?
-4<6-2x<4
Found 2 solutions by richwmiller, jsmallt9:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
Sure ! what do you want to do with it?
Dance or go out to eat?
Treat it as two separate inequalities and see what you can do.
-4<6-2x
-10<-2x
What happens if we divide by -2?
Do we change the direction of the sign?
5>x
6-2x<4
-2x<-2
Again what happens with the sign ?
x>1
combine them
5>x>1
Let's try a few in the original
We want something between 1 and 5
let x=2
-4<6-2x<4
-4<6-4<4
-4<2<4
That is true
Let's go higher
let x=4
-4<6-2x<4
-4<6-2(4)<4
-4<-2<4
that works too
now let's try one we know is too low
let x=0
-4<6-2x<4
-4<6<4
6 is not < 4
good it doesn't work
now one too high
let x=6
-4<6-2x<4
-4<6-12<4
-4<-6<4
but -6 is NOT > -4
so we tried two that should work and they do and two that shouldn't work and they don't

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Here's one way:
-4<6-2x<4
Rewrite the problem as a compound inequality:
-4 < 6-2x and 6-2x < 4
Add -6 to both sides of both inequalities:
-10 < -2x and -2x < -2
Divide both sides by -2 (remembering the special rule to reverse the inequality whenever multiplying or dividing both sides of it by any negative number):
5 > x and x > 1
This should be an acceptable solution. But you could rewrite this in the same format as the original problem:
5 > x > 1
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